Systems and Methods for Efficient Trainable Template Optimization on Low Dimensional Manifolds for Use in Signal Detection

Abstract

Disclosed are systems, methods, computer program products, and other implementations, including a method for signal detection is disclosed that includes obtaining samples of observation data comprising a signal component produced by a source object, and a noise component, and generating based on at least one of the samples of the observation data, processed by a machine learning template derivation system, a filtering template to separate the signal component from the noise component, with the machine learning template derivation system including one or more trainable layers, and with at least one layer of the one or more trainable layers implementing a respective one of one or more iterations of an unrolled optimization process to determine optimized template parameters for the filtering template. The method further includes applying the filtering template to one or more of the samples of the observation data to obtain the signal component of the observation data.

What is claimed is: 
     
         1 . A method for signal detection, the method comprising:
 obtaining samples of observation data comprising a signal component produced by a source object, and a noise component;   generating based on at least one of the samples of the observation data, processed by a machine learning template derivation system, a filtering template to separate the signal component from the noise component, wherein the machine learning template derivation system comprises one or more trainable layers, with at least one layer of the one or more trainable layers implementing a respective one of one or more iterations of an unrolled optimization process to determine optimized template parameters for the filtering template; and   applying the filtering template to one or more of the samples of the observation data to obtain the signal component of the observation data.   
     
     
         2 . The method of  claim 1 , wherein the observation data is representative of signals measured in a high-dimensional signal space, and wherein the signal component produced by the source object occupies a low-dimensional submanifold of the high-dimensional signal space. 
     
     
         3 . The method of  claim 1 , wherein the unrolled optimization process comprises a gradient descent optimization process. 
     
     
         4 . The method of  claim 3 , wherein generating the filtering template comprises:
 determining, in response to the at least one of the samples of the observation data, layer output parameters representing a resultant respective Jacobian matrix and step size information for a respective one of the one or more iterations of the gradient descent optimization process implemented by the one or more layers of the machine learning template derivation system.   
     
     
         5 . The method of  claim 4 , wherein the resultant respective Jacobian matrix and step size for the respective one of the one or more iterations of the gradient descent optimization process are represented by a collection of resultant layer output lookup matrices, W. 
     
     
         6 . The method of  claim 4 , wherein determining the layer output parameters comprises:
 applying the trained parameter values of the at least one layer of the machine learning template derivation system to the at least one of the samples of the observation data, and further to a previously determined set of values of the template parameters, ξ k−1 , to generate the layer output parameters representing the resultant respective Jacobian matrix and the step size information for the respective one of the one or more iterations of the gradient descent optimization process.   
     
     
         7 . The method of  claim 6 , further comprising:
 combining the layer output parameters with the previously determined set of values of the template parameters to produce a next set of values of template parameters, ξ k .   
     
     
         8 . The method of  claim 7 , wherein the next set of values of the template parameters, ξ k , is produced by a last layer of the machine learning, with ξ k  representing the final template parameters for the filtering template. 
     
     
         9 . The method of  claim 7 , wherein the next set of values of template parameters, ξ k  , is produced by a first layer of the machine learning template derivation system, with the previously determined set of values of the template parameters, ξ k−1  representing an initial estimate, ξ 0 , of the template parameters for the filtering template. 
     
     
         10 . The method of  claim 7 , further comprising:
 providing the next set of values of template parameters, ξ k , and the at least one of the samples of the observation data to a next at least one layer of the one or more layers of the machine learning template derivation system to determine a further next set of values of template parameters, ξ k+1 .   
     
     
         11 . The method of  claim 1 , wherein the samples of observation data comprise samples of gravitationally-produced observation data comprising a gravitational waves data component. 
     
     
         12 . The method of  claim 1 , wherein the machine learning template derivation system comprises a neural-network-based machine learning template derivation system. 
     
     
         13 . The method of  claim 1 , further comprising:
 training, prior to obtaining the samples of observation data, the one or more layers of the machine learning template derivation system with training data, the training data comprising input data representing observation samples, and output data representing ground truth data associated with the input data, wherein the ground truth data includes one or more of: template parameters computed in response to the training data using a matched filtering technique, or previously determined template parameters that were used for the input data.   
     
     
         14 . A signal detection system comprising:
 one or more memory storage devices; and   a processor-based device in electrical communication with the one or more memory storage devices, the processor-based device configured to:
 obtain samples of observation data comprising a signal component produced by a source object, and a noise component; 
 generate based on at least one of the samples of the observation data, processed by a machine learning template derivation system, a filtering template to separate the signal component from the noise component, wherein the machine learning template derivation system comprises one or more trainable layers, with at least one layer of the one or more trainable layers implementing a respective one of one or more iterations of an unrolled optimization process to determine optimized template parameters for the filtering template; and 
 apply the filtering template to one or more of the samples of the observation data to obtain the signal component of the observation data. 
   
     
     
         15 . The system of  claim 14 , wherein the unrolled optimization process comprises a gradient descent optimization process. 
     
     
         16 . The system of  claim 15 , wherein the processor-based device configured to generate the filtering template is configured to:
 determine, in response to the at least one of the samples of the observation data, layer output parameters representing a resultant respective Jacobian matrix and step size information for a respective one of the one or more iterations of the gradient descent optimization process implemented by the one or more layers of the machine learning template derivation system.   
     
     
         17 . The system of  claim 15 , wherein the processor-based device configured to determine the layer output parameters is configured to:
 apply the trained parameter values of the at least one layer of the machine learning template derivation system to the at least one of the samples of the observation data, and further to a previously determined set of values of the template parameters, ξ k−1 , to generate the layer output parameters representing the resultant respective Jacobian matrix and the step size information for the respective one of the one or more iterations of the gradient descent optimization process.   
     
     
         18 . The system of  claim 17 , wherein the processor-based device is further configured to:
 combine the layer output parameters with the previously determined set of values of the template parameters to produce a next set of values of template parameters, ξ k .   
     
     
         19 . The system of  claim 18 , wherein the processor-based device is further configured to:
 provide the next set of values of template parameters, ξ k , and the at least one of the samples of the observation data to a next at least one layer of the one or more layers of the machine learning template derivation system to determine a further next set of values of template parameters, ξ k+1 .   
     
     
         20 . Non-transitory computer readable media comprising computer instructions executable on a processor-based device to:
 obtain samples of observation data comprising a signal component produced by a source object, and a noise component;   generate based on at least one of the samples of the observation data, processed by a machine learning template derivation system, a filtering template to separate the signal component from the noise component, wherein the machine learning template derivation system comprises one or more trainable layers, with at least one layer of the one or more trainable layers implementing a respective one of one or more iterations of an unrolled optimization process to determine optimized template parameters for the filtering template; and   apply the filtering template to one or more of the samples of the observation data to obtain the signal component of the observation data.